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Specifying RealTime FiniteState Systems in Linear Logic
 In 2nd International Workshop on Constraint Programming for TimeCritical Applications and MultiAgent Systems (COTIC
, 1998
"... Realtime finitestate systems may be specified in linear logic by means of linear implications between conjunctions of fixed finite length. In this setting, where time is treated as a dense linear ordering, safety properties may be expressed as certain provability problems. These provability proble ..."
Abstract

Cited by 12 (4 self)
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Realtime finitestate systems may be specified in linear logic by means of linear implications between conjunctions of fixed finite length. In this setting, where time is treated as a dense linear ordering, safety properties may be expressed as certain provability problems. These provability problems are shown to be in pspace. They are solvable, with some guidance, by finite proof search in concurrent logic programming environments based on linear logic and acting as sort of modelcheckers. One advantage of our approach is that either it provides unsafe runs or it actually establishes safety. 1 Introduction There are a number of formalisms for expressing realtime processes, including [1, 6, 7, 3, 4, 5, 50, 44, 45, 38]. Many of these realtime formalisms are based on temporal logic or its variations [46, 38, 33] or on timed process algebras [14, 42, 43, 23, 12], or on Buchi automata [52, 3]. In some cases exact complexitytheoretic information is available, such as [51, 3, 5], while ...
Relating StateBased and ProcessBased Concurrency through Linear Logic
, 2006
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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Cited by 12 (1 self)
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired to Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception).
The Logical Meeting Point of Multiset Rewriting and Process Algebra
, 2004
"... Abstract. We present a revisited semantics for multiset rewriting founded on the left sequent rules of linear logic in its LV presentation. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. It drops the distinction between multiset eleme ..."
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Cited by 5 (1 self)
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Abstract. We present a revisited semantics for multiset rewriting founded on the left sequent rules of linear logic in its LV presentation. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. It drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication and more. The cut rules introduce finite auxiliary rewriting chains and are admissible. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. A simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception). The language of ωmultisets forms the basis for the security protocol specification language MSR 3. With relations to both multiset rewriting and process algebra, it supports specifications that are processbased, statebased, or of a mixed nature. Additionally, its deep logical underpinning makes it an ideal common ground for systematically comparing protocol specification languages, a task currently done in an adhoc manner.
Linear Concurrent Constraint Programming Over Reals
, 1998
"... . We introduce a constraint system LC that handles arithmetic constraints over reals within the linear concurrent constraint programming (lcc) framework. This approach provides us with a general, extensible foundation for linear programming algorithm design that comes with a (linear) logical semant ..."
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Cited by 2 (0 self)
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. We introduce a constraint system LC that handles arithmetic constraints over reals within the linear concurrent constraint programming (lcc) framework. This approach provides us with a general, extensible foundation for linear programming algorithm design that comes with a (linear) logical semantics. In particular, it allows us to build a `glassbox' version of the (constraint solver) simplex algorithm by defining (monotone) cc ask and tell agents over a higherlevel constraint system as lcc(LC) programs. We illustrate at the same time the use of the lccframework as a nontrivial concurrent algorithm specification tool. 1 Introduction Constraintbased programming languages are based on a functional separation between a program that successively generates pieces of partial information called constraints, and a constraint solver that collects, combines, simplifies and detects inconsistencies between these constraints. Initially, constraint solvers were monolithic programs written in...
through Linear Logic
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
Abstract
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired by Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic and observe that, possibly modulo duality, they invariably target a small semantic fragment of linear logic that we call LV obs. In the second part of the paper, we propose a new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of
A Concurrent Extension of Functional Logic Programming Languages
, 1999
"... We present a concurrent extension of functional logic programming languages together with a compositional semantics based on labelled sequences, which takes into account the environment of the program. This framework allows to specify, at a very high level, applications that need concurrency and int ..."
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We present a concurrent extension of functional logic programming languages together with a compositional semantics based on labelled sequences, which takes into account the environment of the program. This framework allows to specify, at a very high level, applications that need concurrency and interaction with the environment. For that, we introduce the possibility of defining processes (agents) which specify the dynamics (evolution) of a classical functional logic program, including its communication with the environment. The resulting formalism integrates in a uniform way the main features of functional, logic and concurrent programming.
Expressiveness and Complexity of Concurrent Constraint Programming: a Finite Model Theoretic Approach
, 1998
"... We study the expressiveness and complexity of concurrent constraint programming languages over finite domains. We establish strong connections between these languages and query languages in finite model theory. The bridge to finite model theory yields new (and sometimes quite surprising) results on ..."
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We study the expressiveness and complexity of concurrent constraint programming languages over finite domains. We establish strong connections between these languages and query languages in finite model theory. The bridge to finite model theory yields new (and sometimes quite surprising) results on the expressiveness and complexity of concurrent constraint languages, including several powerful normal forms. These results provide new insight into the impact of various semantics and features of concurrent constraint programming languages on their expressiveness and complexity.